There are no codimension 1 linear isometries on the ball and polydisk algebras
Let \(B_n\) be the open unit ball in \(\mathbb{C}^n\) and \(S_n\) be the boundary. Let \(A(S_n)\) be the space of all complex valued continuous functions on \(S\) which can be extended holomorphically to \(B_n\).NEWLINENEWLINENEWLINEThe main result of this paper is to show that \(A(S_n)\) does not admit codimension 1 linear isometries for all \(n>1\). Also similar results will hold for unit polydiscs.
scientific article; zbMATH DE number 1679389